A trade buys 800 kgs of tomatoes for Rs 7200. 10% tomatoes are damaged in transportion. At what rate per kg) should he sell the rest earn 30% profit ?

Options

A. 9
B. 13
C. 10
D. 12

Answer

To solve the problem step by step, we need to determine how much the trader should sell the remaining tomatoes for in order to earn a 30% profit.

### Step 1: Calculate the total cost of tomatoes
The trader buys 800 kgs of tomatoes for Rs. 7200.

**Cost Price (CP) = Rs. 7200**

### Step 2: Calculate the quantity of tomatoes damaged
10% of the tomatoes are damaged during transportation.

**Damaged tomatoes = 10% of 800 kgs = 0.10 × 800 = 80 kgs**

### Step 3: Calculate the remaining quantity of tomatoes
To find out how many tomatoes are left after the damage:

**Remaining tomatoes = Total tomatoes - Damaged tomatoes = 800 kgs - 80 kgs = 720 kgs**

### Step 4: Calculate the cost price of the remaining tomatoes
The cost price of the remaining tomatoes is the same as the total cost price since the cost is fixed regardless of the quantity lost.

**Cost Price of remaining tomatoes = Rs. 7200**

### Step 5: Calculate the desired selling price for a 30% profit
To find the selling price (SP) that gives a 30% profit, we use the formula:

**Selling Price (SP) = Cost Price (CP) + Profit**

Where Profit = 30% of CP.

**Profit = 30% of Rs. 7200 = 0.30 × 7200 = Rs. 2160**

Now, we can find the selling price:

**SP = CP + Profit = Rs. 7200 + Rs. 2160 = Rs. 9360**

### Step 6: Calculate the selling price per kg of the remaining tomatoes
To find the selling price per kg, we divide the total selling price by the quantity of remaining tomatoes:

**Selling Price per kg = Total Selling Price / Remaining Quantity = Rs. 9360 / 720 kgs**

Calculating this gives:

**Selling Price per kg = Rs. 13**

### Final Answer
The trader should sell the remaining tomatoes at Rs. 13 per kg to earn a 30% profit.

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